2013/05/14 by Christian Bayer, Håkon Hoel, Bayer, Christian +9
Computer Science · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Primary: 81Q20 #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Secondary: 82C10 #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.1305.3330
openalex publication_date 2013/05/14 · openalex created_date 2022/10/02 · openalex updated_date 2026/08/01
The difference of the values of observables for the time-independent\nSchroedinger equation, with matrix valued potentials, and the values of\nobservables for ab initio Born-Oppenheimer molecular dynamics, of the ground\nstate, depends on the probability to be in excited states and the\nelectron/nuclei mass ratio. The paper first proves an error estimate (depending\non the electron/nuclei mass ratio and the probability to be in excited states)\nfor this difference of microcanonical observables, assuming that molecular\ndynamics space-time averages converge, with a rate related to the maximal\nLyapunov exponent. The error estimate is uniform in the number of particles and\nthe analysis does not assume a uniform lower bound on the spectral gap of the\nelectron operator and consequently the probability to be in excited states can\nbe large. A numerical method to determine the probability to be in excited\nstates is then presented, based on Ehrenfest molecular dynamics and stability\nanalysis of a perturbed eigenvalue problem.\n